A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
That is, Y has a gamma distribution with parameters α = 2 and θ. Let 
denote the MLE of θ. Suppose that three such components, tested independently, had lifetimes of 120, 130, and 128 hours.
a Find the MLE of θ.
b Find E() and V(
).
c Suppose that actually equals 130. Give an approximate bound that you might expect for the error of estimation.
d What is the MLE for the variance of Y?
Homework Answers
page 1
page
2Add Answer to:
A certain type of electronic component has a lifetime Y (in hours) with probability density function given by
2. A certain type of electronic component has a lifetime X (in hours) with probability density...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2)...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
2) The lifetime in years of a certain type of electronic component has a probability density...
2) The lifetime in years of a certain type of electronic component has a probability density function given by: otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years.
The probability density function of X, the lifetime of a certain type of electronic device (measured...
The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by fX(x) = ( C/x^2 x>5 0 x<5 where C>0 is a constant which needs to be determined. (i) What is the probability that the device’s lifetime is 10 hours? (ii) Find the 25%th quantile of X? (iii) If the device lifetime is X, then its total electricity cost equals . What is the expected total electricity cost of the...
QUESTION 1 The length of life of an electronic component used in a guidance control system...
QUESTION 1 The length of life of an electronic component used in a guidance control system for missiles is assumed to follow a Weibull distribution with density given by >0, θ > 0 Let Yı,Y2, ,Y10 denote a random variables for the lifetime of a sample of size n= 10 of these electronic components. We wish to construct a 95% confidence interval for θ (a) Find the maximum likelihood estimator, 6, of 0. (b) Find the distribution of U =...
You are given the following probability density function, 6x(r), for the cosine of the surface an...
You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...
2. A certain type of electronic component has a lifetime X (in hours) with probability density function given by otherwise. where θ 0. Let X1, . . . , Xn denote a simple random sample of n such electrical components. . Find an expression for the MLE of θ as a function of X1 Denote this MLE by θ ·Determine the expected value and variance of θ. » What is the MLE for the variance of X? Show that θ...
The lifetime of an electronic component, L, is known to have a variance of 72 (hours2) (a) Using Chebyshev's Inequality, find a lower bound on the probability that the lifetimes are within 20 hours of the mean (b) Suppose it is found that the lifetimes actually follow an exponential distribution Determine the eract probability that the lifetimes are within 20 hours of the mean
2) The lifetime in years of a certain type of electronic component has a probability density function given by: otherwise a) If the expected value of the random variable is 3/5 i.e. E(X)-3/5, find a and b. b) Show that the median lifetime is approximately 0.6501 years.
QUESTION 1 The length of life of an electronic component used in a guidance control system for missiles is assumed to follow a Weibull distribution with density given by >0, θ > 0 Let Yı,Y2, ,Y10 denote a random variables for the lifetime of a sample of size n= 10 of these electronic components. We wish to construct a 95% confidence interval for θ (a) Find the maximum likelihood estimator, 6, of 0. (b) Find the distribution of U =...
You are given the following probability density function, 6x(r), for the cosine of the surface angle, S, of a laser etching tool. The distribution function has one parameter, a, and one constant, c. -1sxs1 a) What is the value of the constant, e? b) What is the moment estimator for a? c) Explain how you can determine if this moment estimator is unbiased. t... . 24) denote a random sample of sample size n 24 with sample mean of-0.01 and...
Most questions answered within 3 hours.
-
For the reaction 1N2+3H2-----> 2NH3, would the reaction rate
trend be: delta[NH3]/ delta t = -2...
asked 16 minutes ago -
A sock stuck to the side of a clothes-dryer barrel has a
centripetal acceleration of 24...
asked 1 hour ago -
A perfect gas undergoes an isentropic process such that its
volume doubles. If the ratio of...
asked 1 hour ago -
list the elements in groups 3A to 6A in the same order as in the
periodic...
asked 1 hour ago -
Estimating effect size. Peng and Chen (2014)
evaluated effect size estimates for various tests. In their...
asked 1 hour ago -
Write a script in MySQL that creates and calls a stored
procedure name test. This procedure...
asked 1 hour ago -
If we test the following: H0: μ = 17
vs. H1: μ ≠ 17 and the...
asked 1 hour ago -
in the past year TVG had revenues of 3 million, cost
of goods sold of $25...
asked 2 hours ago -
4) In a polypeptide, which bond cannot rotate because of its
partial double bond character?
The...
asked 2 hours ago -
Assume that in the short run L = 1,000 and K = 100. 1. What is...
asked 2 hours ago -
At a given temperature, 2.06 atm of H2 and 3.7 atm of Br2 are
mixed and...
asked 2 hours ago -
Sodium reacts with Hydrochloric acid to form sodium chloride and
hydrogen gas. 2Na(s)+ 2 HCl(aq)-> 2...
asked 2 hours ago